Survey and Review -- The work of Anthony Joseph in classical representation theory -- Quantized representation theory following Joseph -- Research Articles -- Opérateurs différentiels invariants et problème de Noether -- Langlands parameters for Heisenberg modules -- Instanton counting via affine Lie algebras II: From Whittaker vectors to the Seiberg-Witten prepotential -- Irreducibility of perfect representations of double affine Hecke algebras -- Algebraic groups over a 2-dimensional local field: Some further constructions -- Modules with a Demazure flag -- Microlocalization of ind-sheaves -- Endoscopic decomposition of certain depth zero representations -- Odd family algebras -- Gelfand-Zeitlin theory from the perspective of classical mechanics. I -- Extensions of algebraic groups -- Differential operators and cohomology groups on the basic affine space -- A q-analogue of an identity of N. Wallach -- Centralizers in the quantum plane algebra -- Centralizer construction of the Yangian of the queer Lie superalgebra -- Definitio nova algebroidis verticiani.

Dedicated to Anthony Joseph, this volume contains surveys and invited articles by leading specialists in representation theory. The focus here is on semisimple Lie algebras and quantum groups, where the impact of Joseph's work has been seminal and has changed the face of the subject. Two introductory biographical overviews of Joseph's contributions in classical representation theory (the theory of primitive ideals in semisimple Lie algebras) and quantized representation theory (the study of the quantized enveloping algebra) are followed by 16 research articles covering a number of varied and interesting topics in representation theory. Contributors: J. Alev; A. Beilinson; A. Braverman; I. Cherednik; J. Dixmier; F. Dumas; P. Etingof; D. Farkas; D. Gaitsgory; F. Ivorra; A. Joseph; D. Joseph; M. Kashiwara; D. Kazhdan; A.A. Kirillov; B. Kostant; S. Kumar; G. Letzter; T. Levasseur; G. Lusztig; L. Makar-Limanov; W. McGovern; M. Nazarov; K-H. Neeb; L.G. Rybnikov; P. Schapira; V. Schechtman; A. Sergeev; J.T. Stafford; Ya. Varshavsky; N. Wallach; and I. Waschkies.

9780817644789

10.1007/0-8176-4478-4 doi

Mathematics.

Group theory.

Topological groups.

Lie groups.

Harmonic analysis.

Geometry.

Mathematics.

Topological Groups, Lie Groups.

Group Theory and Generalizations.

Abstract Harmonic Analysis.

Geometry.

QA252.3 QA387

512.55 512.482